On the Solvability of Systems of Pseudodifferential Operators
(2008) In Rapport TVBM / Avdelningen för byggnadsmaterial, Tekniska högskolan i Lund- Abstract
- We study the solvability for a system of pseudodifferential operators. We will assume that the systems is of principal type, i.e., the principal symbol vanishes of first order on the kernel, and that the eigenvalue close to zero has constant multiplicity. We prove that local solvability is to condition (PSI) on the eigenvalues as in the scalar case. This condition rules out any sign changes from
- to + of the imaginary part of the eigenvalue when going in the positive direction on the bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of 3/2 derivatives (compared with the elliptic case). But we need no conditions on the lower order terms.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/810522
- author
- Dencker, Nils LU
- organization
- publishing date
- 2008
- type
- Other contribution
- publication status
- unpublished
- subject
- keywords
- principal type, systems of pseudodifferential operators, constant characteristics, solvability
- in
- Rapport TVBM / Avdelningen för byggnadsmaterial, Tekniska högskolan i Lund
- pages
- 38 pages
- external identifiers
-
- other:arXiv:0801.4043
- ISSN
- 0348-7911
- language
- English
- LU publication?
- yes
- id
- 789a4d3a-84f2-4c08-956f-4b123a4d7723 (old id 810522)
- alternative location
- http://www.maths.lth.se/matematiklu/personal/dencker/papers/sysolv.pdf
- date added to LUP
- 2016-04-04 11:28:00
- date last changed
- 2019-06-24 11:27:03
@misc{789a4d3a-84f2-4c08-956f-4b123a4d7723,
abstract = {{We study the solvability for a system of pseudodifferential operators. We will assume that the systems is of principal type, i.e., the principal symbol vanishes of first order on the kernel, and that the eigenvalue close to zero has constant multiplicity. We prove that local solvability is to condition (PSI) on the eigenvalues as in the scalar case. This condition rules out any sign changes from<br/><br>
- to + of the imaginary part of the eigenvalue when going in the positive direction on the bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of 3/2 derivatives (compared with the elliptic case). But we need no conditions on the lower order terms.}},
author = {{Dencker, Nils}},
issn = {{0348-7911}},
keywords = {{principal type; systems of pseudodifferential operators; constant characteristics; solvability}},
language = {{eng}},
series = {{Rapport TVBM / Avdelningen för byggnadsmaterial, Tekniska högskolan i Lund}},
title = {{On the Solvability of Systems of Pseudodifferential Operators}},
url = {{http://www.maths.lth.se/matematiklu/personal/dencker/papers/sysolv.pdf}},
year = {{2008}},
}